The Slichter modes of the rotating Earth: a test of the subseismic approximation

Abstract

SUMMARY The eigenperiods of the principal translational (Slichter) mode of free oscillation of the solid inner core (split into a triplet by the Earth's rotation) are computed by a variational principle based on the subseismic approximation, neglecting ellipticity but taking Coriolis coupling into account to high order in the liquid core. First-order Coriolis coupling is retained in the solid parts of the Earth to compute their dynamical response (represented by load Love numbers) to disturbances of the outer core. A simple analytical model explains the presence of a low-frequency resonance in the Love numbers of degree 1 for the inner core boundary, which renders them highly frequency dependent near the Slichter eigenfrequencies. For PREM, with the outer core density profile slightly modified so as to be exactly neutral, the Slichter period neglecting Earth's rotation is 5.4119 hr. Fifth-order Coriolis coupling in the outer core is more than adequate to ensure convergence of the computed eigenperiods: we obtain 5.9697 hr, 5.3017 hr and 4.7594 hr for the prograde equatorial, axial and retrograde equatorial modes respectively. We draw attention to some shortcomings of the subseismic approximation encountered in this study.